Universal Extinction Formula for the System of Maxwell Equations under Local Excitation

Based on the mathematical analysis of the solution of the system of Maxwell equations for the boundary value problem of excitation of a nonlocal scatterer located near a transparent substrate by an electric dipole of arbitrary polarization, a universal formula for the extinction cross-section is obtained. The formula permits one to determine the extinction cross-section by calculating the scattered field at a single point. The result is generalized to the case of excitation of a scatterer by a multipole of arbitrary order in the presence of a transparent substrate; in this case, the multipole can be located both near the scatterer and inside the substrate. Based on the studies carried out, a formula for calculating the fluorescence quantum yield is obtained that eliminates the need to calculate the absorption cross-section for a scatterer with a nonlocality effect.